Hello,
as I have to use artificial light like you, I hope I can provide some useful suggestions. I am lazy so I have skipped all the steps that I don't think necessary.
For the seeds I use a very simple plastic propagator with boxes 35 by 35 mm (1.5") with holes in the bottom. I fold half a standard tissue (for sneezing) on the bottom of each box and insert one seed. Put the whole plate of 32 containers in a transparent plastic box with a lid to prevent drying. When the seeds germinate and are tall enough, I gradually fill the boxes with Gramoflor Sowing Mixture - probably not available in the US, but any high quality sowing mixture will do. When they have 2 or more genuine leaves, I carefully pull the content out, including the tissue, and put it in a plastic container 1/2 - 1 liter in size. In that way I don't disturb the roots at all. The key is that I stopped using commercial soil mixtures as they are not reliably sterilized. I make and sterilize my own mixture: 3.5l = 1 gallon of my garden soil, 1.5 liter of the sowing mixture mentioned above, 4 trowelfuls of Perlite (amorphous volcanic glass) and some sand to taste (the amounts are not that important). I sterilize the mixture in an electric pot for preserving vegetables etc. in one-gallon jars. 160 min at 95°C. After that I add 1 - 1.5 spoonfuls of a very all-purpose fertilizer called Cererit in our country. Essential elements and important micro nutrients. And that's it. I believe that my mixture can be replaced with something commercial with a similar composition. And if you can rely on proper sterilization, so much the better.
There's one very important thing: the balance between the ambient temperature and the intensity of light. I grow my seedlings under about 3,000 lx, so the temperature can be up to 20°C. If the light is dimmer, it's necessary to lower the temperature or you'll get small Eiffel Towers.
One more tip: before sowing, dip the seeds in room-temperature water for 30 - 60 minutes. I also add a few grains of potassium permanganate (just to make it lightly pink), but my friends tell me it's not necessary. Either way, dipping speeds up the germination process. Success rate: 80 - 90%.
I am new here, so I don't know yet how to send a picture. I'll try later today.
Milan HP